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O F F I C I A L S P O N S O R

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Calibration Methods for Minimizing Uncertainties in

Ultrasonic Meters

Calibration Methods for Minimizing Uncertainties in Ultrasonic Meters ¤ M. Narain, GNV Sridhar & V. Singhal

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Kuwait 3rd Flow Measurement Technology Conference

19-21 November, Hilton Resort - Kuwait

Mohit Narain, GNV Sridhar & Vineet Singhal Kuwait Oil Company

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Speaker’s Profile

G.N.V.Sridhar is an instrument engineer working in Operations Technical Support Team

(Gas) of KOC. He has 27 years of vast experience in the field of instrumentation, control

systems, metering etc. His experience covers all of instrumentation & process control.

Presently his role in OTS(Gas) is to ensure the compliance of EPC projects to

specifications & company / international standards.

Holds a bachelor’s degree in Instrumentation from Shivaji Univ., India and has presented

at various international conferences.


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Presentation Outline

Item Slide #

Introduction 6

Calibration Factor Adjustment Methods 7

Flow Weighted Mean Error 8

Polynomial Curve Fitting 12

Multipoint Linearization (of Data) 18

Conclusion 22

User’s Point of View 21

Have We Reached 22


21

6

Introduction

Inherent uncertainty emerges during all lab calib’ns

This ‘raw error’ needs to be ‘adjusted’

The re-adjusted flow-meter is re-verified


20

7

Calibration Factor Adjustment Methods

Flow-Meter adjustment methods, post calibration:

Flow Weighted Mean Error (FWME)

Polynomial Curve Fitting

Multipoint or Piecewise Linearization


19

8

FWME Determination


17

qref qact wfi=qact/qmax** Ei=

100*(qAct-qref)/qAct Pi=

(qact/qmax)*Ei Eicf=

((Ei+100)*F)-100 Picorr=

(qact/qmax)*Eicf

M3/hr M3/hr Flow fraction Error % Flow Weighted Error

Corrected Error %

Corrected Flow Weighted Error%

155.000 153.000 0.025 -1.290 -0.03236383 -1.243 -0.031

311.000 308.380 0.051 -0.842 -0.04258898 -0.795 -0.040

605.000 603.360 0.099 -0.271 -0.02681237 -0.224 -0.022

1575.000 1575.035 0.258 0.002 0.00057378 0.050 0.013

3076.000 3077.100 0.504 0.036 0.01803924 0.083 0.042

4540.100 4539.540 0.744 -0.012 -0.00917920 0.035 0.026

6100.170 6098.015 1.000 -0.035 -0.03531539 0.012 0.012

Sum 2.681 -0.12765 0.000

FWME = Σpi/Σwfi= -0.047610656 **qmax=6100 *Calibration Factor "F"=1.000476333 *F= 100/(100+FWME)

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Impact of FWME on Readings


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Flow % Ref Flow M3/hr

Before Correction After Correction

Flow Reading M3/hr

Error % Flow Reading

M3/hr Error %

0.025 155.000 153.000 -1.290323 153.073 -1.243326

0.051 311.000 308.380 -0.842444 308.527 -0.795234

0.099 605.000 603.360 -0.271074 603.647 -0.223593

0.258 1575.000 1575.035 0.002222 1575.785 0.049834

0.505 3076.000 3077.100 0.035761 3078.565 0.083388

0.745 4540.100 4539.540 -0.012335 4541.701 0.035270

1.000 6100.170 6098.015 -0.035327 6100.918 0.012267

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Impact of FWME on Readings


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0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

ERRO

R

Q / QMAX

Before correction

After correction

11

Flow Weighted Mean Error

Applies a constant bias to the flow readings

Easy to implement

Effective

If meter output is linear in operational range

To correct systematic errors

Not so effective for correction of random errors

Can be used if higher measurement error at lower ranges is acceptable.


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12

Polynomial Curve Fitting (PCF)


Tries to fit the meter output into a curve

The following is a generic nth order equation:

P=a0+(a1*Xn)+(a2*Xn-1)+(a3*Xn-2)+(a4*Xn-3)+(a5*Xn-4)….

n=6(max)

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13

PCF (Linear Curve Fit)


-1.290

-0.842

-0.271

0.002 0.036

-0.012 -0.035

y = 0.9257x - 0.6994

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Erro

r %

Q / Qmax

13

14

PCF (2nd Order PC Fit)


y = -2.9002x2 + 3.7413x - 0.9958

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Erro

r% Q / Qmax

12

15

PCF (4th Order PC Fit)


y = -26.843x4 + 62.941x3 - 50.463x2 + 15.882x - 1.5585

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Erro

r %

Q / Qmax

11

16

PCF (6th Order PC Fit)


y = 250.72x6 - 528.41x5 + 285.23x4 + 64.181x3 - 94.272x2 + 24.362x - 1.8433

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.000 0.200 0.400 0.600 0.800 1.000 1.200

Erro

r %

Q / Qmax

10

17

Polynomial Curve Fitting (PCF)


Does not consider any single point / range Instantaneous corrected readings may have more

inaccuracies compared to uncorrected values When flow is continuously varying error may get

minimized; but cannot be quantified

Higher order may produce undesirable oscillation of values as evident in the 2nd/4th/6th order trend line

There is no single meter factor for tracking the

meter performance over a period of time

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18

Multipoint Linearization (ML)


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19

Multipoint Linearization (ML)


Piecewise linear or multipoint adjustment

Linear interpolation bet’n successive calib’n points

No bias applied to the readings

No single meter factor or calibration factor

Slope of error curve between 2 successive calib’n points determines the correction factor

Unique correction factor at every flowrate

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20

Multipoint Lineariz’n (Before & After)


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Flow % Ref Flow M3/hr

Before Correction After Correction

Flow Reading M3/hr

Error % Flow Reading

M3/hr Error %

0.025 155.000 153.000 -1.290323 155.000 0

0.051 311.000 308.380 -0.842444 311.000 0

0.099 605.000 603.360 -0.271074 605.000 0

0.258 1,575.000 1575.035 0.002222 1575.000 0

0.504 3,076.000 3077.100 0.035761 3076.000 0

0.744 4,540.100 4539.540 -0.012335 4540.100 0

1.000 6,100.170 6098.015 -0.035327 6100.170 0

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Multipoint Lineariz’n (Before & After)


4

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

ERRO

R

Q / QMAX

Before correction

After correction

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Conclusion


Multipoint Linearization or piecewise linearization is a clear winner as:

Error minimized through out the range of the meter

A small meter-error can result in huge $ in long run

No additional cost for implementation

3

23

User’s Point of View


High repeatability alone is not everything Include the calibration adjustment-method in meter

specifications. Ensure the first wet calib’n report gives all the data

along with adjustment-method applied & parameters

Protect calibration data for tracking meter-drift

Calibration be carried out at normal optg. range in addition to flow-rates prescribed by standards.

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24

Have We Reached


Paradigm method

Flow-meter fidelity post-calibration?

Which jargons to follow:

Accuracy

Repeatability

Uncertainty

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25

Thank You


W E A R E D O N E ! ! !

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